Mathematical formulation of mode-to-mode energy transfers and energy fluxes in compressible turbulence

TL;DR

This paper introduces a new mathematical framework for analyzing energy transfers in compressible turbulence, enabling detailed decomposition of energy exchanges among modes and establishing universal analogies with other flow types.

Contribution

The paper presents a novel formalism for mode-to-mode energy transfer rates in compressible turbulence, capturing detailed energy conservation and decomposing transfers into various components.

Findings

Framework captures detailed energy conservation within triads.

Decomposition into rotational, compressive, and mixed components.

Establishes analogies with incompressible and MHD flows.

Abstract

Understanding compressible turbulence is critical for modeling atmospheric, astrophysical, and engineering flows. However, compressible turbulence poses a more significant challenge than incompressible turbulence. We present a novel mathematical framework to compute \textit{mode-to-mode energy transfer rates} and energy fluxes for compressible flows. The formalism captures detailed energy conservation within triads and allows decomposition of transfers into rotational, compressive, and mixed components, providing a clear picture of energy exchange among velocity and internal energy modes. We also establish analogies with incompressible hydrodynamic and magnetohydrodynamic flows, highlighting the framework's universality in studying energy transfers.